Various forms of QMEs can be derived depending on the underlying physical situation or assumptions. When a system is weakly coupled to the environment, the Born-Markov approximation can be applied [1]}, [2]}, from which the Redfield equation can be derived [3]}. This master equation can also be obtained from the more formal Nakajima-Zwanzig time-convolutionless “projection operator perturbation expansion” [4]}, [5]} via truncation at the second order of the interaction strength between the system and bath. However, the Redfield equation does not guarantee complete positivity of the density matrix, which may give rise to unphysical solutions. The most general form of the Markovian QME that preserves the positivity is known as the Lindblad equation [6]}, [7]}. A weak coupling limit [8]}, [9]}, which amounts to the so-called secular approximation, is needed to obtain the QME in Lindblad form from the Redfield equation.
